Quality of life is strongly correlated with power consumption. The geo-disciplines have a crucial role to play in the energy challenge by contributing solutions to all kind of energy resources from resource recovery to energy and waste storage. Energy geoengineering requires a broad understanding of physical processes (sediments, fractured rocks and complex multiphase fluids), coupled phenomena, constitutive models for extreme conditions, and wide-ranging spatial and time scales. Numerical methods are critical for the analysis, design, and optimal operation of energy geosystems under both short and long-term conditions. Furthermore, they allow “numerical experiments” at temporal and spatial scales that are unattainable in the laboratory. Yet, computer power can provide a false sense of reality and unjustified confidence; simulations face uncertainties related to the validation of complex multi-physics codes, limited data, excessive numbers of degrees of freedom, ill-conditioning, and uncertain model parameters. Dimensional analyses help identify the governing processes and allow for simpler and more reliable simulations. Educational programs must evolve to address the knowledge needs in energy geoscience and engineering.